You Might Not Need jQuery

$(el).addClass(className);

if (el.classList)
  el.classList.add(className);
else
  el.className += ' ' + className;

el.classList.add(className);

el.insertAdjacentHTML('afterend', htmlString);

$(el).before(htmlString);

el.insertAdjacentHTML('beforebegin', htmlString);

var children = [];
for (var i = el.children.length; i--;) {
  // Skip comment nodes on IE8
  if (el.children[i].nodeType != 8)
    children.unshift(el.children[i]);
}

el !== child && el.contains(child);

$(el).find(selector).length;

el.querySelector(selector) !== null

$(selector).each(function(i, el){

});

function forEachElement(selector, fn) {
  var elements = document.querySelectorAll(selector);
  for (var i = 0; i < elements.length; i++)
    fn(elements[i], i);
}

forEachElement(selector, function(el, i){

});

var elements = document.querySelectorAll(selector);
Array.prototype.forEach.call(elements, function(el, i){

});

while(el.firstChild)
  el.removeChild(el.firstChild);

$(selector).filter(filterFn);

function filter(selector, filterFn) {
  var elements = document.querySelectorAll(selector);
  var out = [];
  for (var i = elements.length; i--;) {
    if (filterFn(elements[i]))
      out.unshift(elements[i]);
  }
  return out;
}

filter(selector, filterFn);

Array.prototype.filter.call(document.querySelectorAll(selector), filterFn);

el.querySelectorAll(selector);

$('.my #awesome selector');

document.querySelectorAll('.my #awesome selector');

el.getAttribute('tabindex');

$('
').append($(el).clone()).html();

// Varies based on the properties being retrieved, some can be retrieved from el.currentStyle
// https://github.com/jonathantneal/Polyfills-for-IE8/blob/master/getComputedStyle.js

getComputedStyle(el)[ruleName];

el.textContent || el.innerText

$(el).hasClass(className);

if (el.classList)
  el.classList.contains(className);
else
  new RegExp('(^| )' + className + '( |$)', 'gi').test(el.className);

el.classList.contains(className);

var matches = function(el, selector) {
  var _matches = (el.matches || el.matchesSelector || el.msMatchesSelector || el.mozMatchesSelector || el.webkitMatchesSelector || el.oMatchesSelector);

  if (_matches) {
    return _matches.call(el, selector);
  } else {
    var nodes = el.parentNode.querySelectorAll(selector);
    for (var i = nodes.length; i--;) {
      if (nodes[i] === el)
        return true;
    }
    return false;
  }
};

matches(el, '.my-class');

var matches = function(el, selector) {
  return (el.matches || el.matchesSelector || el.msMatchesSelector || el.mozMatchesSelector || el.webkitMatchesSelector || el.oMatchesSelector).call(el, selector);
};

matches(el, '.my-class');

// nextSibling can include text nodes
function nextElementSibling(el) {
  do { el = el.nextSibling; } while ( el && el.nodeType !== 1 );
  return el;
}

el.nextElementSibling || nextElementSibling(el);

var rect = el.getBoundingClientRect()

{
  top: rect.top + document.body.scrollTop,
  left: rect.left + document.body.scrollLeft
}

function outerHeight(el) {
  var height = el.offsetHeight;
  var style = el.currentStyle || getComputedStyle(el);

  height += parseInt(style.marginTop) + parseInt(style.marginBottom);
  return height;
}

outerHeight(el);

function outerHeight(el) {
  var height = el.offsetHeight;
  var style = getComputedStyle(el);

  height += parseInt(style.marginTop) + parseInt(style.marginBottom);
  return height;
}

outerHeight(el);

function outerWidth(el) {
  var width = el.offsetWidth;
  var style = el.currentStyle || getComputedStyle(el);

  width += parseInt(style.marginLeft) + parseInt(style.marginRight);
  return width;
}

outerWidth(el);

function outerWidth(el) {
  var width = el.offsetWidth;
  var style = getComputedStyle(el);

  width += parseInt(style.marginLeft) + parseInt(style.marginRight);
  return width;
}

outerWidth(el);

{left: el.offsetLeft, top: el.offsetTop}

var offset = el.offset();

{
  top: offset.top - document.body.scrollTop,
  left: offset.left - document.body.scrollLeft
}

el.getBoundingClientRect()

parent.insertBefore(el, parent.firstChild);

// prevSibling can include text nodes
function previousElementSibling(el) {
  do { el = el.previousSibling; } while ( el && el.nodeType !== 1 );
  return el;
}

el.previousElementSibling || previousElementSibling(el);

el.previousElementSibling

$(el).attr('tabindex', 3);

el.setAttribute('tabindex', 3);

$(el).css('border-width', '20px');

// Use a class if possible
el.style.borderWidth = '20px';

if (el.textContent !== undefined)
  el.textContent = string;
else
  el.innerText = string;

var siblings = Array.prototype.slice.call(el.parentNode.children);

for (var i = siblings.length; i--;) {
  if (siblings[i] === el) {
    siblings.splice(i, 1);
    break;
  }
}

Array.prototype.filter.call(el.parentNode.children, function(child){
  return child !== el;
});

$(el).toggleClass(className);

if (el.classList) {
  el.classList.toggle(className);
} else {
    var classes = el.className.split(' ');
    var existingIndex = -1;
    for (var i = classes.length; i--;) {
      if (classes[i] === className)
        existingIndex = i;
    }

    if (existingIndex >= 0)
      classes.splice(existingIndex, 1);
    else
      classes.push(className);

  el.className = classes.join(' ');
}

if (el.classList) {
  el.classList.toggle(className);
} else {
  var classes = el.className.split(' ');
  var existingIndex = classes.indexOf(className);

  if (existingIndex >= 0)
    classes.splice(existingIndex, 1);
  else
    classes.push(className);

  el.className = classes.join(' ');
}

el.classList.toggle(className);